LMFDB - Embedded newform 729.2.g.c.676.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			676.3
Character	$\chi$	$=$	729.676
Dual form			729.2.g.c.55.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.588281 - 1.36379i) q^{2} +(-0.141360 + 0.149832i) q^{4} +(-0.0932044 + 1.60026i) q^{5} +(-1.85061 + 0.438602i) q^{7} +(-2.50387 - 0.911335i) q^{8} +O(q^{10})$	\(q+(-0.588281 - 1.36379i) q^{2} +(-0.141360 + 0.149832i) q^{4} +(-0.0932044 + 1.60026i) q^{5} +(-1.85061 + 0.438602i) q^{7} +(-2.50387 - 0.911335i) q^{8} +(2.23724 - 0.814290i) q^{10} +(-3.38752 + 2.22800i) q^{11} +(1.67851 - 0.196189i) q^{13} +(1.68684 + 2.26582i) q^{14} +(0.254067 + 4.36216i) q^{16} +(4.14727 + 3.47997i) q^{17} +(3.70167 - 3.10607i) q^{19} +(-0.226595 - 0.240177i) q^{20} +(5.03133 + 3.30916i) q^{22} +(0.651612 + 0.154435i) q^{23} +(2.41405 + 0.282162i) q^{25} +(-1.25499 - 2.17371i) q^{26} +(0.195884 - 0.339282i) q^{28} +(-2.85835 + 3.83943i) q^{29} +(1.39576 + 4.66216i) q^{31} +(1.03731 - 0.520955i) q^{32} +(2.30618 - 7.70319i) q^{34} +(-0.529392 - 3.00233i) q^{35} +(-2.07926 + 11.7921i) q^{37} +(-6.41363 - 3.22105i) q^{38} +(1.69174 - 3.92190i) q^{40} +(-4.00621 + 9.28743i) q^{41} +(7.64192 + 3.83792i) q^{43} +(0.145031 - 0.822509i) q^{44} +(-0.172714 - 0.979511i) q^{46} +(0.0578400 - 0.193199i) q^{47} +(-3.02305 + 1.51823i) q^{49} +(-1.03533 - 3.45825i) q^{50} +(-0.207877 + 0.279228i) q^{52} +(2.48138 - 4.29788i) q^{53} +(-3.24965 - 5.62856i) q^{55} +(5.03340 + 0.588321i) q^{56} +(6.91768 + 1.63952i) q^{58} +(1.58520 + 1.04260i) q^{59} +(0.124028 + 0.131462i) q^{61} +(5.53710 - 4.64618i) q^{62} +(5.37384 + 4.50919i) q^{64} +(0.157509 + 2.70433i) q^{65} +(-7.95826 - 10.6898i) q^{67} +(-1.10767 + 0.129468i) q^{68} +(-3.78311 + 2.48819i) q^{70} +(9.41216 - 3.42575i) q^{71} +(-10.9327 - 3.97917i) q^{73} +(17.3051 - 4.10138i) q^{74} +(-0.0578765 + 0.993701i) q^{76} +(5.29176 - 5.60894i) q^{77} +(-1.45390 - 3.37053i) q^{79} -7.00426 q^{80} +15.0229 q^{82} +(-2.17367 - 5.03914i) q^{83} +(-5.95539 + 6.31235i) q^{85} +(0.738510 - 12.6797i) q^{86} +(10.5124 - 2.49148i) q^{88} +(-6.65218 - 2.42120i) q^{89} +(-3.02021 + 1.09927i) q^{91} +(-0.115251 + 0.0758017i) q^{92} +(-0.297508 + 0.0347738i) q^{94} +(4.62550 + 6.21312i) q^{95} +(0.0778051 + 1.33586i) q^{97} +(3.84894 + 3.22965i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.588281	−	1.36379i	−0.415977	−	0.964344i	−0.989418	−	0.145096i	$-0.953651\pi$
$2$	−0.588281	−	1.36379i	−0.415977	−	0.964344i	0.573440	−	0.819247i	$-0.305608\pi$
$3$		0			0
$3$		0			0
$4$	−0.141360	+	0.149832i	−0.0706798	+	0.0749162i
$5$	−0.0932044	+	1.60026i	−0.0416823	+	0.715657i	0.911134	+	0.412110i	$0.135208\pi$
$5$	−0.0932044	+	1.60026i	−0.0416823	+	0.715657i	−0.952816	+	0.303547i	$0.901829\pi$
$6$		0			0
$7$	−1.85061	+	0.438602i	−0.699465	+	0.165776i	−0.564937	−	0.825134i	$-0.691100\pi$
$7$	−1.85061	+	0.438602i	−0.699465	+	0.165776i	−0.134527	+	0.990910i	$0.542952\pi$
$8$	−2.50387	−	0.911335i	−0.885253	−	0.322206i
$9$		0			0
$10$	2.23724	−	0.814290i	0.707478	−	0.257501i
$11$	−3.38752	+	2.22800i	−1.02137	+	0.671769i	−0.945592	−	0.325356i	$-0.894516\pi$
$11$	−3.38752	+	2.22800i	−1.02137	+	0.671769i	−0.0757828	+	0.997124i	$0.524146\pi$
$12$		0			0
$13$	1.67851	−	0.196189i	0.465534	−	0.0544131i	0.119907	−	0.992785i	$-0.461740\pi$
$13$	1.67851	−	0.196189i	0.465534	−	0.0544131i	0.345627	+	0.938372i	$0.387666\pi$
$14$	1.68684	+	2.26582i	0.450826	+	0.605565i
$15$		0			0
$16$	0.254067	+	4.36216i	0.0635167	+	1.09054i
$17$	4.14727	+	3.47997i	1.00586	+	0.844017i	0.987785	−	0.155820i	$-0.0498020\pi$
$17$	4.14727	+	3.47997i	1.00586	+	0.844017i	0.0180743	+	0.999837i	$0.494246\pi$
$18$		0			0
$19$	3.70167	−	3.10607i	0.849220	−	0.712581i	−0.110397	−	0.993888i	$-0.535212\pi$
$19$	3.70167	−	3.10607i	0.849220	−	0.712581i	0.959618	+	0.281307i	$0.0907679\pi$
$20$	−0.226595	−	0.240177i	−0.0506682	−	0.0537052i
$21$		0			0
$22$	5.03133	+	3.30916i	1.07268	+	0.705515i
$23$	0.651612	+	0.154435i	0.135870	+	0.0322019i	0.297988	−	0.954570i	$-0.403684\pi$
$23$	0.651612	+	0.154435i	0.135870	+	0.0322019i	−0.162118	+	0.986771i	$0.551832\pi$
$24$		0			0
$25$	2.41405	+	0.282162i	0.482811	+	0.0564325i
$26$	−1.25499	−	2.17371i	−0.246124	−	0.426300i
$27$		0			0
$28$	0.195884	−	0.339282i	0.0370187	−	0.0641182i
$29$	−2.85835	+	3.83943i	−0.530782	+	0.712965i	−0.983947	−	0.178462i	$-0.942888\pi$
$29$	−2.85835	+	3.83943i	−0.530782	+	0.712965i	0.453164	+	0.891427i	$0.350295\pi$
$30$		0			0
$31$	1.39576	+	4.66216i	0.250686	+	0.837349i	0.987002	+	0.160711i	$0.0513786\pi$
$31$	1.39576	+	4.66216i	0.250686	+	0.837349i	−0.736316	+	0.676638i	$0.763436\pi$
$32$	1.03731	−	0.520955i	0.183372	−	0.0920927i
$33$		0			0
$34$	2.30618	−	7.70319i	0.395507	−	1.32109i
$35$	−0.529392	−	3.00233i	−0.0894836	−	0.507487i
$36$		0			0
$37$	−2.07926	+	11.7921i	−0.341829	+	1.93861i	0.00314382	+	0.999995i	$0.498999\pi$
$37$	−2.07926	+	11.7921i	−0.341829	+	1.93861i	−0.344973	+	0.938613i	$0.612112\pi$
$38$	−6.41363	−	3.22105i	−1.04043	−	0.522523i
$39$		0			0
$40$	1.69174	−	3.92190i	0.267488	−	0.620107i
$41$	−4.00621	+	9.28743i	−0.625664	+	1.45045i	0.250344	+	0.968157i	$0.419456\pi$
$41$	−4.00621	+	9.28743i	−0.625664	+	1.45045i	−0.876009	+	0.482296i	$0.839803\pi$
$42$		0			0
$43$	7.64192	+	3.83792i	1.16538	+	0.585277i	0.922961	−	0.384895i	$-0.125762\pi$
$43$	7.64192	+	3.83792i	1.16538	+	0.585277i	0.242421	+	0.970171i	$0.422059\pi$
$44$	0.145031	−	0.822509i	0.0218642	−	0.123998i
$45$		0			0
$46$	−0.172714	−	0.979511i	−0.0254653	−	0.144421i
$47$	0.0578400	−	0.193199i	0.00843683	−	0.0281810i	−0.953667	−	0.300863i	$-0.902725\pi$
$47$	0.0578400	−	0.193199i	0.00843683	−	0.0281810i	0.962104	+	0.272682i	$0.0879106\pi$
$48$		0			0
$49$	−3.02305	+	1.51823i	−0.431864	+	0.216890i
$50$	−1.03533	−	3.45825i	−0.146418	−	0.489070i
$51$		0			0
$52$	−0.207877	+	0.279228i	−0.0288274	+	0.0387219i
$53$	2.48138	−	4.29788i	0.340844	−	0.590359i	−0.643746	−	0.765240i	$-0.722621\pi$
$53$	2.48138	−	4.29788i	0.340844	−	0.590359i	0.984590	+	0.174880i	$0.0559538\pi$
$54$		0			0
$55$	−3.24965	−	5.62856i	−0.438183	−	0.758955i
$56$	5.03340	+	0.588321i	0.672617	+	0.0786177i
$57$		0			0
$58$	6.91768	+	1.63952i	0.908336	+	0.215280i
$59$	1.58520	+	1.04260i	0.206375	+	0.135735i	0.648489	−	0.761224i	$-0.275401\pi$
$59$	1.58520	+	1.04260i	0.206375	+	0.135735i	−0.442114	+	0.896959i	$0.645771\pi$
$60$		0			0
$61$	0.124028	+	0.131462i	0.0158802	+	0.0168320i	0.735265	−	0.677780i	$-0.237058\pi$
$61$	0.124028	+	0.131462i	0.0158802	+	0.0168320i	−0.719385	+	0.694612i	$0.755576\pi$
$62$	5.53710	−	4.64618i	0.703212	−	0.590065i
$63$		0			0
$64$	5.37384	+	4.50919i	0.671730	+	0.563648i
$65$	0.157509	+	2.70433i	0.0195366	+	0.335431i
$66$		0			0
$67$	−7.95826	−	10.6898i	−0.972256	−	1.30597i	−0.951976	−	0.306172i	$-0.900952\pi$
$67$	−7.95826	−	10.6898i	−0.972256	−	1.30597i	−0.0202796	−	0.999794i	$-0.506456\pi$
$68$	−1.10767	+	0.129468i	−0.134324	+	0.0157003i
$69$		0			0
$70$	−3.78311	+	2.48819i	−0.452168	+	0.297396i
$71$	9.41216	−	3.42575i	1.11702	−	0.406561i	0.283455	−	0.958985i	$-0.408519\pi$
$71$	9.41216	−	3.42575i	1.11702	−	0.406561i	0.833563	+	0.552424i	$0.186297\pi$
$72$		0			0
$73$	−10.9327	−	3.97917i	−1.27957	−	0.465726i	−0.389282	−	0.921119i	$-0.627277\pi$
$73$	−10.9327	−	3.97917i	−1.27957	−	0.465726i	−0.890291	+	0.455392i	$0.849499\pi$
$74$	17.3051	−	4.10138i	2.01168	−	0.476776i
$75$		0			0
$76$	−0.0578765	+	0.993701i	−0.00663889	+	0.113985i
$77$	5.29176	−	5.60894i	0.603052	−	0.639198i
$78$		0			0
$79$	−1.45390	−	3.37053i	−0.163577	−	0.379214i	0.816638	−	0.577150i	$-0.195835\pi$
$79$	−1.45390	−	3.37053i	−0.163577	−	0.379214i	−0.980215	+	0.197936i	$0.936576\pi$
$80$	−7.00426			−0.783100
$81$		0			0
$82$	15.0229			1.65900
$83$	−2.17367	−	5.03914i	−0.238592	−	0.553117i	0.756282	−	0.654246i	$-0.227014\pi$
$83$	−2.17367	−	5.03914i	−0.238592	−	0.553117i	−0.994873	+	0.101129i	$0.967755\pi$
$84$		0			0
$85$	−5.95539	+	6.31235i	−0.645953	+	0.684670i
$86$	0.738510	−	12.6797i	0.0796356	−	1.36729i
$87$		0			0
$88$	10.5124	−	2.49148i	1.12062	−	0.265592i
$89$	−6.65218	−	2.42120i	−0.705130	−	0.256646i	−0.0355305	−	0.999369i	$-0.511312\pi$
$89$	−6.65218	−	2.42120i	−0.705130	−	0.256646i	−0.669600	+	0.742722i	$0.733534\pi$
$90$		0			0
$91$	−3.02021	+	1.09927i	−0.316604	+	0.115234i
$92$	−0.115251	+	0.0758017i	−0.0120157	+	0.00790287i
$93$		0			0
$94$	−0.297508	+	0.0347738i	−0.0306857	+	0.00358664i
$95$	4.62550	+	6.21312i	0.474566	+	0.637453i
$96$		0			0
$97$	0.0778051	+	1.33586i	0.00789992	+	0.135636i	0.999952	+	0.00980765i	$0.00312192\pi$
$97$	0.0778051	+	1.33586i	0.00789992	+	0.135636i	−0.992052	+	0.125829i	$0.959841\pi$
$98$	3.84894	+	3.22965i	0.388802	+	0.326244i
$99$		0			0
$100$	−0.383526	+	0.321817i	−0.0383526	+	0.0321817i
$101$	−3.40131	−	3.60518i	−0.338443	−	0.358729i	0.535690	−	0.844415i	$-0.320051\pi$
$101$	−3.40131	−	3.60518i	−0.338443	−	0.358729i	−0.874134	+	0.485686i	$0.838570\pi$
$102$		0			0
$103$	1.90445	+	1.25258i	0.187652	+	0.123420i	0.639859	−	0.768493i	$-0.278993\pi$
$103$	1.90445	+	1.25258i	0.187652	+	0.123420i	−0.452207	+	0.891913i	$0.649363\pi$
$104$	−4.38156	−	1.03845i	−0.429648	−	0.101828i
$105$		0			0
$106$	−7.32115	−	0.855719i	−0.711092	−	0.0831148i
$107$	2.21467	+	3.83593i	0.214101	+	0.370833i	0.952994	−	0.302989i	$-0.0979846\pi$
$107$	2.21467	+	3.83593i	0.214101	+	0.370833i	−0.738893	+	0.673822i	$0.764651\pi$
$108$		0			0
$109$	−9.21824	+	15.9665i	−0.882947	+	1.52931i	−0.0348978	+	0.999391i	$0.511111\pi$
$109$	−9.21824	+	15.9665i	−0.882947	+	1.52931i	−0.848049	+	0.529918i	$0.822223\pi$
$110$	−5.76445	+	7.74301i	−0.549619	+	0.738267i
$111$		0			0
$112$	−2.38343	−	7.96121i	−0.225213	−	0.752264i
$113$	8.05934	−	4.04755i	0.758159	−	0.380762i	−0.0273390	−	0.999626i	$-0.508703\pi$
$113$	8.05934	−	4.04755i	0.758159	−	0.380762i	0.785498	+	0.618865i	$0.212407\pi$
$114$		0			0
$115$	−0.307869	+	1.02835i	−0.0287089	+	0.0958944i
$116$	−0.171216	−	0.971014i	−0.0158970	−	0.0901563i
$117$		0			0
$118$	0.489346	−	2.77522i	0.0450479	−	0.255479i
$119$	−9.20129	−	4.62106i	−0.843481	−	0.423612i
$120$		0			0
$121$	2.15438	−	4.99442i	0.195853	−	0.454038i
$122$	0.106323	−	0.246485i	0.00962604	−	0.0223157i
$123$		0			0
$124$	−0.895846	−	0.449911i	−0.0804493	−	0.0404032i
$125$	−2.06830	+	11.7299i	−0.184994	+	1.04915i
$126$		0			0
$127$	−0.304561	−	1.72725i	−0.0270254	−	0.153269i	0.968309	−	0.249756i	$-0.0803504\pi$
$127$	−0.304561	−	1.72725i	−0.0270254	−	0.153269i	−0.995334	+	0.0964872i	$0.969239\pi$
$128$	3.65408	−	12.2055i	0.322978	−	1.07882i
$129$		0			0
$130$	3.59547	−	1.80571i	0.315344	−	0.158372i
$131$	−2.05452	−	6.86256i	−0.179504	−	0.599585i	−0.999625	−	0.0273945i	$-0.991279\pi$
$131$	−2.05452	−	6.86256i	−0.179504	−	0.599585i	0.820121	−	0.572191i	$-0.193906\pi$
$132$		0			0
$133$	−5.48801	+	7.37168i	−0.475871	+	0.639205i
$134$	−9.89692	+	17.1420i	−0.854964	+	1.48084i
$135$		0			0
$136$	−7.21281	−	12.4930i	−0.618493	−	1.07126i
$137$	17.3549	+	2.02850i	1.48273	+	0.173307i	0.818624	−	0.574329i	$-0.194737\pi$
$137$	17.3549	+	2.02850i	1.48273	+	0.173307i	0.664109	+	0.747636i	$0.268811\pi$
$138$		0			0
$139$	−18.4877	−	4.38167i	−1.56811	−	0.371649i	−0.647478	−	0.762084i	$-0.724176\pi$
$139$	−18.4877	−	4.38167i	−1.56811	−	0.371649i	−0.920630	+	0.390435i	$0.872325\pi$
$140$	0.524681	+	0.345088i	0.0443436	+	0.0291653i
$141$		0			0
$142$	−10.2090	−	10.8209i	−0.856719	−	0.908069i
$143$	−5.24886	+	4.40431i	−0.438931	+	0.368307i
$144$		0			0
$145$	−5.87767	−	4.93195i	−0.488114	−	0.409576i
$146$	1.00474	+	17.2507i	0.0831528	+	1.42768i
$147$		0			0
$148$	−1.47291	−	1.97847i	−0.121073	−	0.162629i
$149$	−7.32320	+	0.855959i	−0.599940	+	0.0701229i	−0.410642	−	0.911797i	$-0.634695\pi$
$149$	−7.32320	+	0.855959i	−0.599940	+	0.0701229i	−0.189298	+	0.981920i	$0.560621\pi$
$150$		0			0
$151$	2.23139	−	1.46761i	0.181588	−	0.119432i	−0.455461	−	0.890256i	$-0.650525\pi$
$151$	2.23139	−	1.46761i	0.181588	−	0.119432i	0.637048	+	0.770824i	$0.280155\pi$
$152$	−12.0992	+	4.40374i	−0.981372	+	0.357190i
$153$		0			0
$154$	−10.7624	−	3.91721i	−0.867262	−	0.315658i
$155$	−7.59075	+	1.79904i	−0.609704	+	0.144502i
$156$		0			0
$157$	0.332250	−	5.70452i	0.0265165	−	0.455270i	−0.958751	−	0.284248i	$-0.908256\pi$
$157$	0.332250	−	5.70452i	0.0265165	−	0.455270i	0.985267	−	0.171022i	$-0.0547069\pi$
$158$	−3.74138	+	3.96563i	−0.297648	+	0.315489i
$159$		0			0
$160$	0.736981	+	1.70851i	0.0582635	+	0.135070i
$161$	−1.27361			−0.100375
$162$		0			0
$163$	16.0381			1.25620			0.628100	−	0.778132i	$-0.283833\pi$
$163$	16.0381			1.25620			0.628100	+	0.778132i	$0.283833\pi$
$164$	−0.825242	−	1.91313i	−0.0644406	−	0.149390i
$165$		0			0
$166$	−5.59359	+	5.92886i	−0.434147	+	0.460168i
$167$	−1.11336	+	19.1157i	−0.0861545	+	1.47922i	0.627445	+	0.778661i	$0.284101\pi$
$167$	−1.11336	+	19.1157i	−0.0861545	+	1.47922i	−0.713599	+	0.700554i	$0.752936\pi$
$168$		0			0
$169$	−9.87069	+	2.33940i	−0.759284	+	0.179954i
$170$	12.1121	+	4.40846i	0.928959	+	0.338113i
$171$		0			0
$172$	−1.65530	+	0.602480i	−0.126216	+	0.0459387i
$173$	19.7483	−	12.9886i	1.50143	−	0.987509i	0.509539	−	0.860448i	$-0.329816\pi$
$173$	19.7483	−	12.9886i	1.50143	−	0.987509i	0.991895	−	0.127061i	$-0.0405544\pi$
$174$		0			0
$175$	−4.59123	+	0.536637i	−0.347064	+	0.0405660i
$176$	−10.5796	−	14.2108i	−0.797464	−	1.07118i
$177$		0			0
$178$	0.611352	+	10.4965i	0.0458228	+	0.786747i
$179$	−3.43489	−	2.88222i	−0.256736	−	0.215427i	0.505331	−	0.862926i	$-0.331371\pi$
$179$	−3.43489	−	2.88222i	−0.256736	−	0.215427i	−0.762066	+	0.647499i	$0.775815\pi$
$180$		0			0
$181$	2.92076	−	2.45081i	0.217098	−	0.182167i	−0.527752	−	0.849398i	$-0.676965\pi$
$181$	2.92076	−	2.45081i	0.217098	−	0.182167i	0.744851	+	0.667231i	$0.232521\pi$
$182$	3.27590	+	3.47225i	0.242826	+	0.257380i
$183$		0			0
$184$	−1.49081	−	0.980522i	−0.109904	−	0.0722850i
$185$	−18.6766	−	4.42643i	−1.37313	−	0.325438i
$186$		0			0
$187$	−21.8023	−	2.54833i	−1.59434	−	0.186352i
$188$	0.0207712	+	0.0359768i	0.00151490	+	0.00262388i
$189$		0			0
$190$	5.75229	−	9.96325i	0.417315	−	0.722810i
$191$	−10.9862	+	14.7571i	−0.794936	+	1.06778i	0.201165	+	0.979557i	$0.435527\pi$
$191$	−10.9862	+	14.7571i	−0.794936	+	1.06778i	−0.996100	+	0.0882265i	$0.971880\pi$
$192$		0			0
$193$	4.71004	+	15.7326i	0.339036	+	1.13246i	0.942259	+	0.334886i	$0.108698\pi$
$193$	4.71004	+	15.7326i	0.339036	+	1.13246i	−0.603223	+	0.797573i	$0.706117\pi$
$194$	1.77606	−	0.891972i	0.127514	−	0.0640398i
$195$		0			0
$196$	0.199856	−	0.667566i	0.0142754	−	0.0476833i
$197$	−3.25113	−	18.4381i	−0.231633	−	1.31366i	−0.849589	−	0.527445i	$-0.823150\pi$
$197$	−3.25113	−	18.4381i	−0.231633	−	1.31366i	0.617956	−	0.786213i	$-0.287961\pi$
$198$		0			0
$199$	0.155470	−	0.881713i	0.0110210	−	0.0625029i	−0.978801	−	0.204812i	$-0.934342\pi$
$199$	0.155470	−	0.881713i	0.0110210	−	0.0625029i	0.989822	+	0.142309i	$0.0454527\pi$
$200$	−5.78734	−	2.90651i	−0.409227	−	0.205521i
$201$		0			0
$202$	−2.91577	+	6.75953i	−0.205153	+	0.475599i
$203$	3.60571	−	8.35897i	0.253071	−	0.586685i
$204$		0			0
$205$	−14.4889	−	7.27659i	−1.01195	−	0.508219i
$206$	0.587899	−	3.33414i	0.0409609	−	0.232301i
$207$		0			0
$208$	1.28226	+	7.27206i	0.0889088	+	0.504227i
$209$	−5.61912	+	18.7692i	−0.388683	+	1.29829i
$210$		0			0
$211$	13.3695	−	6.71439i	0.920391	−	0.462238i	0.0754817	−	0.997147i	$-0.475951\pi$
$211$	13.3695	−	6.71439i	0.920391	−	0.462238i	0.844909	+	0.534909i	$0.179654\pi$
$212$	0.293194	+	0.979338i	0.0201367	+	0.0672612i
$213$		0			0
$214$	3.92854	−	5.27695i	0.268550	−	0.360725i
$215$	−6.85392	+	11.8713i	−0.467433	+	0.809618i
$216$		0			0
$217$	−4.62784	−	8.01565i	−0.314158	−	0.544138i
$218$	27.1978	+	3.17896i	1.84206	+	0.215306i
$219$		0			0
$220$	1.30271	+	0.308748i	0.0878286	+	0.0208158i
$221$	7.64395	+	5.02750i	0.514188	+	0.338186i
$222$		0			0
$223$	4.25530	+	4.51035i	0.284956	+	0.302036i	0.854002	−	0.520270i	$-0.174169\pi$
$223$	4.25530	+	4.51035i	0.284956	+	0.302036i	−0.569046	+	0.822306i	$0.692687\pi$
$224$	−1.69116	+	1.41905i	−0.112995	+	0.0948142i
$225$		0			0
$226$	−10.2612	−	8.61013i	−0.682562	−	0.572737i
$227$	−0.830506	−	14.2592i	−0.0551226	−	0.946419i	−0.906590	−	0.422012i	$-0.861324\pi$
$227$	−0.830506	−	14.2592i	−0.0551226	−	0.946419i	0.851468	−	0.524407i	$-0.175713\pi$
$228$		0			0
$229$	11.6644	+	15.6680i	0.770804	+	1.03537i	0.998104	+	0.0615447i	$0.0196027\pi$
$229$	11.6644	+	15.6680i	0.770804	+	1.03537i	−0.227300	+	0.973825i	$0.572990\pi$
$230$	1.58357	−	0.185093i	0.104417	−	0.0122046i
$231$		0			0
$232$	10.6560	−	7.00853i	0.699598	−	0.460133i
$233$	8.91628	−	3.24526i	0.584125	−	0.212604i	−0.0330187	−	0.999455i	$-0.510512\pi$
$233$	8.91628	−	3.24526i	0.584125	−	0.212604i	0.617143	+	0.786851i	$0.288290\pi$
$234$		0			0
$235$	0.303777	+	0.110566i	0.0198162	+	0.00721252i
$236$	−0.380298	+	0.0901324i	−0.0247553	+	0.00586712i
$237$		0			0
$238$	−0.889207	+	15.2671i	−0.0576387	+	0.989619i
$239$	−7.55122	+	8.00383i	−0.488448	+	0.517725i	−0.923976	−	0.382451i	$-0.875080\pi$
$239$	−7.55122	+	8.00383i	−0.488448	+	0.517725i	0.435528	+	0.900175i	$0.356562\pi$
$240$		0			0
$241$	−0.867612	−	2.01135i	−0.0558878	−	0.129562i	0.887984	−	0.459874i	$-0.152105\pi$
$241$	−0.867612	−	2.01135i	−0.0558878	−	0.129562i	−0.943872	+	0.330312i	$0.892846\pi$
$242$	−8.07871			−0.519319
$243$		0			0
$244$	−0.0372298			−0.00238340
$245$	−2.14780	−	4.97916i	−0.137218	−	0.318107i
$246$		0			0
$247$	5.60389	−	5.93978i	0.356567	−	0.377939i
$248$	0.753987	−	12.9455i	0.0478782	−	0.822038i
$249$		0			0
$250$	17.2138	−	4.07975i	1.08870	−	0.258026i
$251$	6.59388	+	2.39998i	0.416202	+	0.151485i	0.541629	−	0.840618i	$-0.317808\pi$
$251$	6.59388	+	2.39998i	0.416202	+	0.151485i	−0.125427	+	0.992103i	$0.540030\pi$
$252$		0			0
$253$	−2.55143	+	0.928643i	−0.160407	+	0.0583833i
$254$	−2.17644	+	1.43147i	−0.136562	+	0.0898181i
$255$		0			0
$256$	−4.86005	+	0.568059i	−0.303753	+	0.0355037i
$257$	−0.279271	−	0.375126i	−0.0174205	−	0.0233997i	0.793328	−	0.608795i	$-0.208347\pi$
$257$	−0.279271	−	0.375126i	−0.0174205	−	0.0233997i	−0.810748	+	0.585395i	$0.800939\pi$
$258$		0			0
$259$	−1.32414	−	22.7345i	−0.0822778	−	1.41265i
$260$	−0.427461	−	0.358683i	−0.0265100	−	0.0222446i
$261$		0			0
$262$	−8.15045	+	6.83904i	−0.503536	+	0.422517i
$263$	−13.0974	−	13.8824i	−0.807621	−	0.856028i	0.184302	−	0.982870i	$-0.440997\pi$
$263$	−13.0974	−	13.8824i	−0.807621	−	0.856028i	−0.991923	+	0.126842i	$0.959516\pi$
$264$		0			0
$265$	6.64644	+	4.37143i	0.408288	+	0.268535i
$266$	13.2819	+	3.14787i	0.814365	+	0.193008i
$267$		0			0
$268$	2.72665	+	0.318700i	0.166557	+	0.0194677i
$269$	−2.12061	−	3.67300i	−0.129296	−	0.223947i	0.794108	−	0.607776i	$-0.207938\pi$
$269$	−2.12061	−	3.67300i	−0.129296	−	0.223947i	−0.923404	+	0.383830i	$0.874605\pi$
$270$		0			0
$271$	−3.83162	+	6.63656i	−0.232754	+	0.403142i	−0.958618	−	0.284697i	$-0.908107\pi$
$271$	−3.83162	+	6.63656i	−0.232754	+	0.403142i	0.725863	+	0.687839i	$0.241440\pi$
$272$	−14.1265	+	18.9752i	−0.856544	+	1.15054i
$273$		0			0
$274$	−7.44313	−	24.8618i	−0.449656	−	1.50196i
$275$	−8.80630	+	4.42269i	−0.531040	+	0.266698i
$276$		0			0
$277$	−4.25476	+	14.2119i	−0.255644	+	0.853909i	0.729764	+	0.683699i	$0.239630\pi$
$277$	−4.25476	+	14.2119i	−0.255644	+	0.853909i	−0.985408	+	0.170210i	$0.945555\pi$
$278$	4.90030	+	27.7910i	0.293901	+	1.66679i
$279$		0			0
$280$	−1.41060	+	7.99991i	−0.0842995	+	0.478086i
$281$	0.994631	+	0.499522i	0.0593347	+	0.0297990i	0.478219	−	0.878241i	$-0.341282\pi$
$281$	0.994631	+	0.499522i	0.0593347	+	0.0297990i	−0.418884	+	0.908040i	$0.637579\pi$
$282$		0			0
$283$	−2.61783	+	6.06882i	−0.155614	+	0.360754i	−0.978132	−	0.207985i	$-0.933309\pi$
$283$	−2.61783	+	6.06882i	−0.155614	+	0.360754i	0.822518	+	0.568739i	$0.192569\pi$
$284$	−0.817211	+	1.89451i	−0.0484926	+	0.112418i
$285$		0			0
$286$	9.09435	+	4.56735i	0.537760	+	0.270073i
$287$	3.34043	−	18.9445i	0.197179	−	1.11826i
$288$		0			0
$289$	2.13761	+	12.1230i	0.125742	+	0.713117i
$290$	−3.26841	+	10.9173i	−0.191928	+	0.641084i
$291$		0			0
$292$	2.14165	−	1.07557i	0.125330	−	0.0629432i
$293$	−0.892759	−	2.98202i	−0.0521555	−	0.174212i	0.927943	−	0.372721i	$-0.121575\pi$
$293$	−0.892759	−	2.98202i	−0.0521555	−	0.174212i	−0.980099	+	0.198509i	$0.936390\pi$
$294$		0			0
$295$	−1.81618	+	2.43955i	−0.105742	+	0.142036i
$296$	15.9528	−	27.6310i	0.927235	−	1.60602i
$297$		0			0
$298$	5.47544	+	9.48374i	0.317184	+	0.549379i
$299$	1.12403	+	0.131381i	0.0650045	+	0.00759794i
$300$		0			0
$301$	−15.8255	−	3.75072i	−0.912168	−	0.216188i
$302$	−3.31418	−	2.17977i	−0.190710	−	0.125432i
$303$		0			0
$304$	14.4896	+	15.3581i	0.831037	+	0.880848i
$305$	−0.221933	+	0.186224i	−0.0127079	+	0.0106632i
$306$		0			0
$307$	−5.76257	−	4.83537i	−0.328887	−	0.275969i	0.463359	−	0.886171i	$-0.346644\pi$
$307$	−5.76257	−	4.83537i	−0.328887	−	0.275969i	−0.792246	+	0.610202i	$0.791088\pi$
$308$	0.0923596	+	1.58575i	0.00526268	+	0.0903567i
$309$		0			0
$310$	6.91900	+	9.29383i	0.392973	+	0.527854i
$311$	15.2831	−	1.78634i	0.866628	−	0.101294i	0.328851	−	0.944382i	$-0.393338\pi$
$311$	15.2831	−	1.78634i	0.866628	−	0.101294i	0.537777	+	0.843087i	$0.319264\pi$
$312$		0			0
$313$	3.31693	−	2.18158i	0.187484	−	0.123310i	−0.452297	−	0.891867i	$-0.649395\pi$
$313$	3.31693	−	2.18158i	0.187484	−	0.123310i	0.639781	+	0.768557i	$0.279025\pi$
$314$	−7.97521	+	2.90274i	−0.450067	+	0.163811i
$315$		0			0
$316$	0.710537	+	0.258614i	0.0399708	+	0.0145482i
$317$	8.34397	−	1.97756i	0.468644	−	0.111071i	0.0104930	−	0.999945i	$-0.496660\pi$
$317$	8.34397	−	1.97756i	0.468644	−	0.111071i	0.458151	+	0.888874i	$0.348512\pi$
$318$		0			0
$319$	1.12844	−	19.3746i	0.0631805	−	1.08477i
$320$	−7.71673	+	8.17925i	−0.431378	+	0.457234i
$321$		0			0
$322$	0.749242	+	1.73694i	0.0417536	+	0.0967958i
$323$	26.1608			1.45563
$324$		0			0
$325$	4.10736			0.227835
$326$	−9.43490	−	21.8726i	−0.522551	−	1.21141i
$327$		0			0
$328$	18.4950	−	19.6035i	1.02121	−	1.08242i
$329$	−0.0223016	+	0.382905i	−0.00122953	+	0.0211102i
$330$		0			0
$331$	−9.07927	+	2.15183i	−0.499042	+	0.118275i	−0.472425	−	0.881371i	$-0.656621\pi$
$331$	−9.07927	+	2.15183i	−0.499042	+	0.118275i	−0.0266164	+	0.999646i	$0.508473\pi$
$332$	1.06230	+	0.386644i	0.0583010	+	0.0212198i
$333$		0			0
$334$	26.7247	−	9.72699i	1.46231	−	0.532237i
$335$	17.8482	−	11.7389i	0.975150	−	0.641366i
$336$		0			0
$337$	−4.37776	+	0.511687i	−0.238472	+	0.0278734i	−0.234489	−	0.972119i	$-0.575342\pi$
$337$	−4.37776	+	0.511687i	−0.238472	+	0.0278734i	−0.00398267	+	0.999992i	$0.501268\pi$
$338$	8.99717	+	12.0853i	0.489382	+	0.657354i
$339$		0			0
$340$	−0.103942	−	1.78462i	−0.00563706	−	0.0967847i
$341$	−15.1155	−	12.6834i	−0.818548	−	0.686844i
$342$		0			0
$343$	15.1270	−	12.6931i	0.816782	−	0.685362i
$344$	−15.6368	−	16.5740i	−0.843078	−	0.893610i
$345$		0			0
$346$	−29.3313	−	19.2915i	−1.57686	−	1.03712i
$347$	19.4982	+	4.62117i	1.04672	+	0.248077i	0.717777	−	0.696273i	$-0.245160\pi$
$347$	19.4982	+	4.62117i	1.04672	+	0.248077i	0.328943	+	0.944350i	$0.393308\pi$
$348$		0			0
$349$	33.4202	+	3.90626i	1.78894	+	0.209097i	0.944939	−	0.327245i	$-0.106120\pi$
$349$	33.4202	+	3.90626i	1.78894	+	0.209097i	0.844001	+	0.536342i	$0.180194\pi$
$350$	3.43279	+	5.94576i	0.183490	+	0.317814i
$351$		0			0
$352$	−2.35320	+	4.07587i	−0.125426	+	0.217244i
$353$	4.81620	−	6.46927i	0.256340	−	0.344325i	−0.655259	−	0.755404i	$-0.727441\pi$
$353$	4.81620	−	6.46927i	0.256340	−	0.344325i	0.911600	+	0.411079i	$0.134848\pi$
$354$		0			0
$355$	4.60483	+	15.3812i	0.244399	+	0.816349i
$356$	1.30312	−	0.654453i	0.0690654	−	0.0346859i
$357$		0			0
$358$	−1.91005	+	6.38002i	−0.100949	+	0.337194i
$359$	−2.83469	−	16.0764i	−0.149609	−	0.848477i	−0.963550	−	0.267529i	$-0.913793\pi$
$359$	−2.83469	−	16.0764i	−0.149609	−	0.848477i	0.813940	−	0.580948i	$-0.197318\pi$
$360$		0			0
$361$	0.755367	−	4.28390i	0.0397562	−	0.225468i
$362$	−5.06061	−	2.54153i	−0.265980	−	0.133580i
$363$		0			0
$364$	0.262230	−	0.607917i	0.0137446	−	0.0318635i
$365$	7.38667	−	17.1242i	0.386636	−	0.896323i
$366$		0			0
$367$	11.7615	+	5.90686i	0.613947	+	0.308336i	0.728462	−	0.685086i	$-0.240235\pi$
$367$	11.7615	+	5.90686i	0.613947	+	0.308336i	−0.114516	+	0.993421i	$0.536532\pi$
$368$	−0.508116	+	2.88167i	−0.0264874	+	0.150217i
$369$		0			0
$370$	4.95036	+	28.0749i	0.257357	+	1.45954i
$371$	−2.70701	+	9.04204i	−0.140541	+	0.469439i
$372$		0			0
$373$	0.194504	−	0.0976835i	0.0100710	−	0.00505786i	−0.443757	−	0.896147i	$-0.646354\pi$
$373$	0.194504	−	0.0976835i	0.0100710	−	0.00505786i	0.453828	+	0.891090i	$0.350058\pi$
$374$	9.35050	+	31.2329i	0.483503	+	1.61501i
$375$		0			0
$376$	−0.320893	+	0.431034i	−0.0165488	+	0.0222289i
$377$	−4.04451	+	7.00529i	−0.208303	+	0.360791i
$378$		0			0
$379$	12.0931	+	20.9458i	0.621180	+	1.07592i	0.989266	+	0.146124i	$0.0466797\pi$
$379$	12.0931	+	20.9458i	0.621180	+	1.07592i	−0.368086	+	0.929792i	$0.619987\pi$
$380$	−1.58478	−	0.185235i	−0.0812977	−	0.00950234i
$381$		0			0
$382$	26.5885	+	6.30159i	1.36039	+	0.322417i
$383$	7.06738	+	4.64829i	0.361126	+	0.237516i	0.717086	−	0.696985i	$-0.245476\pi$
$383$	7.06738	+	4.64829i	0.361126	+	0.237516i	−0.355960	+	0.934501i	$0.615846\pi$
$384$		0			0
$385$	8.48253	+	8.99096i	0.432310	+	0.458222i
$386$	18.6851	−	15.6787i	0.951048	−	0.798024i
$387$		0			0
$388$	−0.211154	−	0.177179i	−0.0107197	−	0.00899491i
$389$	1.46030	+	25.0723i	0.0740400	+	1.27122i	0.806839	+	0.590772i	$0.201177\pi$
$389$	1.46030	+	25.0723i	0.0740400	+	1.27122i	−0.732799	+	0.680446i	$0.761786\pi$
$390$		0			0
$391$	2.16498	+	2.90807i	0.109488	+	0.147067i
$392$	8.95294	−	1.04645i	0.452192	−	0.0528536i
$393$		0			0
$394$	−23.2330	+	15.2806i	−1.17046	+	0.769826i
$395$	5.52922	−	2.01247i	0.278205	−	0.101258i
$396$		0			0
$397$	23.8173	+	8.66880i	1.19536	+	0.435074i	0.861602	−	0.507585i	$-0.169462\pi$
$397$	23.8173	+	8.66880i	1.19536	+	0.435074i	0.333756	+	0.942660i	$0.391684\pi$
$398$	−1.29393	+	0.306667i	−0.0648588	+	0.0153718i
$399$		0			0
$400$	−0.617506	+	10.6022i	−0.0308753	+	0.530108i
$401$	16.2900	−	17.2664i	0.813483	−	0.862242i	−0.179097	−	0.983831i	$-0.557318\pi$
$401$	16.2900	−	17.2664i	0.813483	−	0.862242i	0.992580	+	0.121589i	$0.0387991\pi$
$402$		0			0
$403$	3.25746	+	7.55163i	0.162265	+	0.376174i
$404$	1.02098			0.0507957
$405$		0			0
$406$	−13.5210			−0.671037
$407$	−19.2293	−	44.5785i	−0.953160	−	2.20967i
$408$		0			0
$409$	−6.44213	+	6.82826i	−0.318543	+	0.337636i	−0.866783	−	0.498685i	$-0.833816\pi$
$409$	−6.44213	+	6.82826i	−0.318543	+	0.337636i	0.548240	+	0.836321i	$0.315298\pi$
$410$	−1.40020	+	24.0404i	−0.0691508	+	1.18727i
$411$		0			0
$412$	−0.456890	+	0.108285i	−0.0225093	+	0.00533481i
$413$	−3.39087	−	1.23418i	−0.166854	−	0.0607298i
$414$		0			0
$415$	8.26652	−	3.00877i	0.405787	−	0.147695i
$416$	1.63892	−	1.07794i	0.0803547	−	0.0528501i
$417$		0			0
$418$	28.9028	−	3.37825i	1.41368	−	0.165236i
$419$	−7.01065	−	9.41694i	−0.342493	−	0.460048i	0.597187	−	0.802102i	$-0.296285\pi$
$419$	−7.01065	−	9.41694i	−0.342493	−	0.460048i	−0.939680	+	0.342054i	$0.888877\pi$
$420$		0			0
$421$	−0.393410	−	6.75459i	−0.0191736	−	0.329199i	−0.994232	−	0.107250i	$-0.965795\pi$
$421$	−0.393410	−	6.75459i	−0.0191736	−	0.329199i	0.975058	−	0.221948i	$-0.0712416\pi$
$422$	−17.0220	−	14.2831i	−0.828618	−	0.695293i
$423$		0			0
$424$	−10.1299	+	8.49998i	−0.491950	+	0.412795i
$425$	9.02980	+	9.57103i	0.438010	+	0.464263i
$426$		0			0
$427$	−0.287187	−	0.188886i	−0.0138980	−	0.00914083i
$428$	−0.887812	−	0.210415i	−0.0429140	−	0.0101708i
$429$		0			0
$430$	20.2220	+	2.36361i	0.975191	+	0.113984i
$431$	3.90563	+	6.76475i	0.188128	+	0.325846i	0.944626	−	0.328149i	$-0.106425\pi$
$431$	3.90563	+	6.76475i	0.188128	+	0.325846i	−0.756498	+	0.653996i	$0.773092\pi$
$432$		0			0
$433$	−2.20878	+	3.82573i	−0.106147	+	0.183853i	−0.914206	−	0.405249i	$-0.867185\pi$
$433$	−2.20878	+	3.82573i	−0.106147	+	0.183853i	0.808059	+	0.589102i	$0.200518\pi$
$434$	−8.20918	+	11.0268i	−0.394053	+	0.529305i
$435$		0			0
$436$	−1.08921	−	3.63820i	−0.0521635	−	0.174238i
$437$	2.89173	−	1.45228i	0.138330	−	0.0694721i
$438$		0			0
$439$	4.31161	−	14.4018i	0.205782	−	0.687360i	−0.791328	−	0.611392i	$-0.790610\pi$
$439$	4.31161	−	14.4018i	0.205782	−	0.687360i	0.997110	−	0.0759684i	$-0.0242048\pi$
$440$	3.00721	+	17.0547i	0.143363	+	0.813052i
$441$		0			0
$442$	2.35966	−	13.3823i	0.112238	−	0.636531i
$443$	10.1485	+	5.09675i	0.482168	+	0.242154i	0.673243	−	0.739422i	$-0.264901\pi$
$443$	10.1485	+	5.09675i	0.482168	+	0.242154i	−0.191075	+	0.981576i	$0.561197\pi$
$444$		0			0
$445$	4.49455	−	10.4195i	0.213062	−	0.493934i
$446$	3.64786	−	8.45668i	0.172731	−	0.400435i
$447$		0			0
$448$	−11.9226	−	5.98776i	−0.563291	−	0.282895i
$449$	−1.16004	+	6.57891i	−0.0547457	+	0.310478i	−0.999868	−	0.0162381i	$-0.994831\pi$
$449$	−1.16004	+	6.57891i	−0.0547457	+	0.310478i	0.945122	+	0.326716i	$0.105942\pi$
$450$		0			0
$451$	−7.12134	−	40.3871i	−0.335331	−	1.90176i
$452$	−0.532810	+	1.77971i	−0.0250613	+	0.0837105i
$453$		0			0
$454$	−18.9580	+	9.52106i	−0.889743	+	0.446846i
$455$	−1.47761	−	4.93557i	−0.0692716	−	0.231383i
$456$		0			0
$457$	7.17351	−	9.63570i	0.335563	−	0.450739i	−0.602030	−	0.798473i	$-0.705641\pi$
$457$	7.17351	−	9.63570i	0.335563	−	0.450739i	0.937593	+	0.347734i	$0.113049\pi$
$458$	14.5059	−	25.1249i	0.677815	−	1.17401i
$459$		0			0
$460$	−0.110560	−	0.191496i	−0.00515490	−	0.00892855i
$461$	−6.95142	−	0.812504i	−0.323760	−	0.0378421i	−0.0473393	−	0.998879i	$-0.515074\pi$
$461$	−6.95142	−	0.812504i	−0.323760	−	0.0378421i	−0.276421	+	0.961037i	$0.589148\pi$
$462$		0			0
$463$	27.2778	+	6.46495i	1.26771	+	0.300452i	0.808827	−	0.588047i	$-0.200103\pi$
$463$	27.2778	+	6.46495i	1.26771	+	0.300452i	0.458879	+	0.888499i	$0.348251\pi$
$464$	−17.4744	−	11.4931i	−0.811229	−	0.533554i
$465$		0			0
$466$	−9.67112	−	10.2508i	−0.448006	−	0.474858i
$467$	−10.9662	+	9.20178i	−0.507458	+	0.425807i	−0.860233	−	0.509900i	$-0.829682\pi$
$467$	−10.9662	+	9.20178i	−0.507458	+	0.425807i	0.352776	+	0.935708i	$0.385238\pi$
$468$		0			0
$469$	19.4162	+	16.2921i	0.896557	+	0.752300i
$470$	−0.0279179	−	0.479331i	−0.00128776	−	0.0221099i
$471$		0			0
$472$	−3.01898	−	4.05519i	−0.138960	−	0.186655i
$473$	−34.4380	+	4.02523i	−1.58346	+	0.185080i
$474$		0			0
$475$	9.81243	−	6.45374i	0.450225	−	0.296118i
$476$	1.99307	−	0.725420i	0.0913524	−	0.0332496i
$477$		0			0
$478$	15.3578	+	5.58977i	0.702448	+	0.255670i
$479$	−21.8904	+	5.18813i	−1.00020	+	0.237052i	−0.697926	−	0.716170i	$-0.745894\pi$
$479$	−21.8904	+	5.18813i	−1.00020	+	0.237052i	−0.302273	+	0.953221i	$0.597745\pi$
$480$		0			0
$481$	−1.17658	+	20.2010i	−0.0536473	+	0.921088i
$482$	−2.23266	+	2.36648i	−0.101695	+	0.107790i
$483$		0			0
$484$	0.443783	+	1.02881i	0.0201720	+	0.0467639i
$485$	−2.14498			−0.0973984
$486$		0			0
$487$	−41.7203			−1.89053			−0.945264	−	0.326307i	$-0.894196\pi$
$487$	−41.7203			−1.89053			−0.945264	+	0.326307i	$0.894196\pi$
$488$	−0.190745	−	0.442196i	−0.00863460	−	0.0200173i
$489$		0			0
$490$	−5.52701	+	5.85829i	−0.249685	+	0.264650i
$491$	0.643607	−	11.0503i	0.0290456	−	0.498694i	−0.952144	−	0.305649i	$-0.901127\pi$
$491$	0.643607	−	11.0503i	0.0290456	−	0.498694i	0.981190	−	0.193045i	$-0.0618363\pi$
$492$		0			0
$493$	−25.2154	+	5.97617i	−1.13565	+	0.269153i
$494$	−11.3973	−	4.14826i	−0.512787	−	0.186639i
$495$		0			0
$496$	−19.9825	+	7.27302i	−0.897239	+	0.326568i
$497$	−15.9157	+	10.4679i	−0.713917	+	0.469550i
$498$		0			0
$499$	−7.76171	+	0.907214i	−0.347462	+	0.0406125i	−0.288034	−	0.957620i	$-0.593002\pi$
$499$	−7.76171	+	0.907214i	−0.347462	+	0.0406125i	−0.0594278	+	0.998233i	$0.518928\pi$
$500$	−1.46514	−	1.96803i	−0.0655232	−	0.0880130i
$501$		0			0
$502$	−0.605994	−	10.4045i	−0.0270468	−	0.464376i
$503$	18.1547	+	15.2336i	0.809478	+	0.679233i	0.950483	−	0.310776i	$-0.100589\pi$
$503$	18.1547	+	15.2336i	0.809478	+	0.679233i	−0.141005	+	0.990009i	$0.545033\pi$
$504$		0			0
$505$	6.08624	−	5.10696i	0.270834	−	0.227257i
$506$	2.76743	+	2.93330i	0.123027	+	0.130401i
$507$		0			0
$508$	0.301851	+	0.198530i	0.0133925	+	0.00880836i
$509$	12.1281	+	2.87442i	0.537570	+	0.127406i	0.490428	−	0.871482i	$-0.336841\pi$
$509$	12.1281	+	2.87442i	0.537570	+	0.127406i	0.0471419	+	0.998888i	$0.484989\pi$
$510$		0			0
$511$	21.9774	+	2.56879i	0.972222	+	0.113636i
$512$	−9.10692	−	15.7736i	−0.402473	−	0.697103i
$513$		0			0
$514$	−0.347303	+	0.601546i	−0.0153189	+	0.0265331i
$515$	−2.18195	+	2.93087i	−0.0961484	+	0.129150i
$516$		0			0
$517$	0.234514	+	0.783332i	0.0103139	+	0.0344509i
$518$	−30.2261	+	15.1801i	−1.32806	+	0.666976i
$519$		0			0
$520$	2.07017	−	6.91484i	0.0907829	−	0.303236i
$521$	3.66734	+	20.7985i	0.160669	+	0.911200i	0.953418	+	0.301652i	$0.0975380\pi$
$521$	3.66734	+	20.7985i	0.160669	+	0.911200i	−0.792749	+	0.609548i	$0.791351\pi$
$522$		0			0
$523$	7.23247	−	41.0174i	0.316254	−	1.79356i	−0.248848	−	0.968543i	$-0.580052\pi$
$523$	7.23247	−	41.0174i	0.316254	−	1.79356i	0.565102	−	0.825021i	$-0.308837\pi$
$524$	1.31866	+	0.662256i	0.0576059	+	0.0289308i
$525$		0			0
$526$	−11.2277	+	26.0288i	−0.489553	+	1.13491i
$527$	−10.4356	+	24.1924i	−0.454581	+	1.05384i
$528$		0			0
$529$	−20.1528	−	10.1211i	−0.876209	−	0.440049i
$530$	2.05173	−	11.6360i	0.0891217	−	0.505434i
$531$		0			0
$532$	−0.328733	−	1.86434i	−0.0142524	−	0.0808293i
$533$	−4.90235	+	16.3750i	−0.212344	+	0.709279i
$534$		0			0
$535$	−6.34489	+	3.18653i	−0.274314	+	0.137766i
$536$	10.1845	+	34.0185i	0.439902	+	1.46938i
$537$		0			0
$538$	−3.76168	+	5.05281i	−0.162177	+	0.217842i
$539$	6.85799	−	11.8784i	0.295395	−	0.511638i
$540$		0			0
$541$	−4.87647	−	8.44629i	−0.209656	−	0.363134i	0.741950	−	0.670455i	$-0.233901\pi$
$541$	−4.87647	−	8.44629i	−0.209656	−	0.363134i	−0.951606	+	0.307320i	$0.900568\pi$
$542$	11.3049	+	1.32136i	0.485588	+	0.0567571i
$543$		0			0
$544$	6.11490	+	1.44926i	0.262174	+	0.0621364i
$545$	−24.6913	−	16.2397i	−1.05766	−	0.695632i
$546$		0			0
$547$	−0.475687	−	0.504198i	−0.0203389	−	0.0215580i	0.717124	−	0.696945i	$-0.245458\pi$
$547$	−0.475687	−	0.504198i	−0.0203389	−	0.0215580i	−0.737463	+	0.675387i	$0.763976\pi$
$548$	−2.75722	+	2.31358i	−0.117783	+	0.0988314i
$549$		0			0
$550$	11.2122	+	9.40814i	0.478089	+	0.401164i
$551$	1.34487	+	23.0905i	0.0572934	+	0.983689i
$552$		0			0
$553$	4.16893	+	5.59984i	0.177281	+	0.238130i
$554$	21.8850	−	2.55799i	0.929804	−	0.108678i
$555$		0			0
$556$	3.26993	−	2.15067i	0.138676	−	0.0912087i
$557$	−28.7125	+	10.4505i	−1.21659	+	0.442801i	−0.868984	−	0.494841i	$-0.835226\pi$
$557$	−28.7125	+	10.4505i	−1.21659	+	0.442801i	−0.347602	+	0.937642i	$0.613004\pi$
$558$		0			0
$559$	13.5800	+	4.94270i	0.574371	+	0.209054i
$560$	12.9621	−	3.07208i	0.547751	−	0.129819i
$561$		0			0
$562$	0.0961204	−	1.65032i	0.00405460	−	0.0696147i
$563$	6.68923	−	7.09017i	0.281918	−	0.298815i	−0.570905	−	0.821016i	$-0.693407\pi$
$563$	6.68923	−	7.09017i	0.281918	−	0.298815i	0.852822	+	0.522201i	$0.174889\pi$
$564$		0			0
$565$	5.72596	+	13.2743i	0.240893	+	0.558453i
$566$	9.81660			0.412622
$567$		0			0
$568$	−26.6889			−1.11984
$569$	−7.79560	−	18.0722i	−0.326808	−	0.757627i	−0.999838	−	0.0180113i	$-0.994267\pi$
$569$	−7.79560	−	18.0722i	−0.326808	−	0.757627i	0.673029	−	0.739616i	$-0.264993\pi$
$570$		0			0
$571$	22.6458	−	24.0031i	0.947697	−	1.00450i	−0.0522860	−	0.998632i	$-0.516651\pi$
$571$	22.6458	−	24.0031i	0.947697	−	1.00450i	0.999983	−	0.00586776i	$-0.00186778\pi$
$572$	0.0820673	−	1.40904i	0.00343140	−	0.0589149i
$573$		0			0
$574$	−27.8014	+	6.58906i	−1.16041	+	0.275022i
$575$	1.52945	+	0.556674i	0.0637824	+	0.0232149i
$576$		0			0
$577$	−19.1279	+	6.96197i	−0.796303	+	0.289831i	−0.707954	−	0.706259i	$-0.750381\pi$
$577$	−19.1279	+	6.96197i	−0.796303	+	0.289831i	−0.0883494	+	0.996090i	$0.528159\pi$
$578$	15.2757	−	10.0470i	0.635384	−	0.417899i
$579$		0			0
$580$	1.56983	−	0.183487i	0.0651837	−	0.00761888i
$581$	6.23280	+	8.37210i	0.258580	+	0.347333i
$582$		0			0
$583$	1.16997	+	20.0877i	0.0484553	+	0.831946i
$584$	23.7477	+	19.9267i	0.982686	+	0.824571i
$585$		0			0
$586$	−3.54165	+	2.97180i	−0.146304	+	0.122764i
$587$	24.1185	+	25.5641i	0.995477	+	1.05514i	0.998478	+	0.0551480i	$0.0175631\pi$
$587$	24.1185	+	25.5641i	0.995477	+	1.05514i	−0.00300161	+	0.999995i	$0.500955\pi$
$588$		0			0
$589$	19.6476	+	12.9224i	0.809566	+	0.532460i
$590$	4.39545	+	1.04174i	0.180958	+	0.0428878i
$591$		0			0
$592$	−51.9672	−	6.07410i	−2.13584	−	0.249644i
$593$	−4.46816	−	7.73909i	−0.183485	−	0.317806i	0.759580	−	0.650414i	$-0.225405\pi$
$593$	−4.46816	−	7.73909i	−0.183485	−	0.317806i	−0.943065	+	0.332608i	$0.892071\pi$
$594$		0			0
$595$	8.25249	−	14.2937i	0.338319	−	0.585986i
$596$	0.906953	−	1.21825i	0.0371503	−	0.0499015i
$597$		0			0
$598$	−0.482071	−	1.61023i	−0.0197134	−	0.0658472i
$599$	−35.4506	+	17.8040i	−1.44847	+	0.727451i	−0.987152	−	0.159782i	$-0.948921\pi$
$599$	−35.4506	+	17.8040i	−1.44847	+	0.727451i	−0.461322	+	0.887233i	$0.652625\pi$
$600$		0			0
$601$	−6.78673	+	22.6693i	−0.276837	+	0.924699i	0.700615	+	0.713539i	$0.252909\pi$
$601$	−6.78673	+	22.6693i	−0.276837	+	0.924699i	−0.977452	+	0.211159i	$0.932276\pi$
$602$	4.19466	+	23.7891i	0.170962	+	0.969572i
$603$		0			0
$604$	−0.0955328	+	0.541794i	−0.00388718	+	0.0220453i
$605$	7.79156	+	3.91307i	0.316772	+	0.159089i
$606$		0			0
$607$	7.03429	−	16.3073i	0.285513	−	0.661893i	−0.713745	−	0.700405i	$-0.753003\pi$
$607$	7.03429	−	16.3073i	0.285513	−	0.661893i	0.999258	+	0.0385121i	$0.0122618\pi$
$608$	2.22164	−	5.15035i	0.0900995	−	0.208874i
$609$		0			0
$610$	0.384529	+	0.193118i	0.0155691	+	0.00781911i
$611$	0.0591812	−	0.335633i	0.00239422	−	0.0135783i
$612$		0			0
$613$	−0.410662	−	2.32898i	−0.0165865	−	0.0940666i	0.975391	−	0.220483i	$-0.0707635\pi$
$613$	−0.410662	−	2.32898i	−0.0165865	−	0.0940666i	−0.991977	+	0.126417i	$0.959652\pi$
$614$	−3.20441	+	10.7035i	−0.129319	+	0.431957i
$615$		0			0
$616$	−18.3615	+	9.22150i	−0.739807	+	0.371545i
$617$	−9.69418	−	32.3808i	−0.390273	−	1.30360i	−0.897204	−	0.441616i	$-0.854405\pi$
$617$	−9.69418	−	32.3808i	−0.390273	−	1.30360i	0.506931	−	0.861986i	$-0.330780\pi$
$618$		0			0
$619$	28.3599	−	38.0940i	1.13988	−	1.53113i	0.330537	−	0.943793i	$-0.392770\pi$
$619$	28.3599	−	38.0940i	1.13988	−	1.53113i	0.809345	−	0.587334i	$-0.199823\pi$
$620$	0.803470	−	1.39165i	0.0322681	−	0.0558901i
$621$		0			0
$622$	−11.4270	−	19.7921i	−0.458180	−	0.793591i
$623$	13.3725	+	1.56303i	0.535759	+	0.0626213i
$624$		0			0
$625$	−6.75322	−	1.60054i	−0.270129	−	0.0640217i
$626$	−4.92649	−	3.24021i	−0.196902	−	0.129505i
$627$		0			0
$628$	0.807755	+	0.856170i	0.0322329	+	0.0341649i
$629$	−49.6594	+	41.6692i	−1.98005	+	1.66146i
$630$		0			0
$631$	−14.6874	−	12.3242i	−0.584695	−	0.490617i	0.301790	−	0.953374i	$-0.402416\pi$
$631$	−14.6874	−	12.3242i	−0.584695	−	0.490617i	−0.886485	+	0.462757i	$0.846860\pi$
$632$	0.568709	+	9.76436i	0.0226220	+	0.388406i
$633$		0			0
$634$	−7.60557	−	10.2161i	−0.302056	−	0.405731i
$635$	2.79244	−	0.326389i	0.110814	−	0.0129523i
$636$		0			0
$637$	−4.77634	+	3.14145i	−0.189246	+	0.124469i
$638$	−27.0866	+	9.85872i	−1.07237	+	0.390311i
$639$		0			0
$640$	19.1913	+	6.98507i	0.758603	+	0.276109i
$641$	2.04822	−	0.485436i	0.0808997	−	0.0191736i	−0.189967	−	0.981791i	$-0.560838\pi$
$641$	2.04822	−	0.485436i	0.0808997	−	0.0191736i	0.270866	+	0.962617i	$0.412690\pi$
$642$		0			0
$643$	2.54772	−	43.7427i	0.100472	−	1.72504i	−0.452433	−	0.891798i	$-0.649444\pi$
$643$	2.54772	−	43.7427i	0.100472	−	1.72504i	0.552905	−	0.833244i	$-0.313519\pi$
$644$	0.180037	−	0.190829i	0.00709447	−	0.00751970i
$645$		0			0
$646$	−15.3899	−	35.6778i	−0.605507	−	1.40372i
$647$	2.17952			0.0856859			0.0428430	−	0.999082i	$-0.486358\pi$
$647$	2.17952			0.0856859			0.0428430	+	0.999082i	$0.486358\pi$
$648$		0			0
$649$	−7.69281			−0.301969
$650$	−2.41628	−	5.60157i	−0.0947743	−	0.219712i
$651$		0			0
$652$	−2.26714	+	2.40303i	−0.0887880	+	0.0941098i
$653$	1.08815	−	18.6828i	0.0425826	−	0.731115i	−0.907680	−	0.419664i	$-0.862148\pi$
$653$	1.08815	−	18.6828i	0.0425826	−	0.731115i	0.950262	−	0.311451i	$-0.100815\pi$
$654$		0			0
$655$	11.1734	−	2.64814i	0.436579	−	0.103471i
$656$	−41.5311	−	15.1161i	−1.62152	−	0.590183i
$657$		0			0
$658$	0.535320	−	0.194841i	0.0208689	−	0.00759568i
$659$	11.9512	−	7.86043i	0.465553	−	0.306199i	−0.294974	−	0.955505i	$-0.595311\pi$
$659$	11.9512	−	7.86043i	0.465553	−	0.306199i	0.760527	+	0.649306i	$0.224941\pi$
$660$		0			0
$661$	−24.8243	+	2.90155i	−0.965555	+	0.112857i	−0.584234	−	0.811586i	$-0.698605\pi$
$661$	−24.8243	+	2.90155i	−0.965555	+	0.112857i	−0.381321	+	0.924443i	$0.624531\pi$
$662$	8.27579	+	11.1163i	0.321648	+	0.432048i
$663$		0			0
$664$	0.850255	+	14.5983i	0.0329963	+	0.566524i
$665$	−11.2851	−	9.46931i	−0.437617	−	0.367204i
$666$		0			0
$667$	−2.45548	+	2.06039i	−0.0950764	+	0.0797786i
$668$	−2.70676	−	2.86900i	−0.104728	−	0.111005i
$669$		0			0
$670$	−26.5091	−	17.4353i	−1.02414	−	0.673586i
$671$	−0.713045	−	0.168995i	−0.0275268	−	0.00652397i
$672$		0			0
$673$	29.4895	+	3.44683i	1.13674	+	0.132866i	0.663576	−	0.748109i	$-0.269038\pi$
$673$	29.4895	+	3.44683i	1.13674	+	0.132866i	0.473163	+	0.880975i	$0.343112\pi$
$674$	3.27319	+	5.66933i	0.126078	+	0.218374i
$675$		0			0
$676$	1.04480	−	1.80964i	0.0401846	−	0.0696017i
$677$	23.1605	−	31.1099i	0.890129	−	1.19565i	−0.0897310	−	0.995966i	$-0.528601\pi$
$677$	23.1605	−	31.1099i	0.890129	−	1.19565i	0.979860	−	0.199685i	$-0.0639919\pi$
$678$		0			0
$679$	−0.729900	−	2.43803i	−0.0280110	−	0.0935632i
$680$	20.6642	−	10.3780i	0.792436	−	0.397977i
$681$		0			0
$682$	−8.40530	+	28.0757i	−0.321856	+	1.07507i
$683$	−2.81006	−	15.9367i	−0.107524	−	0.609799i	−0.990182	−	0.139784i	$-0.955359\pi$
$683$	−2.81006	−	15.9367i	−0.107524	−	0.609799i	0.882658	−	0.470016i	$-0.155752\pi$
$684$		0			0
$685$	−4.86369	+	27.5833i	−0.185832	+	1.05391i
$686$	−26.2096	−	13.1630i	−1.00069	−	0.502564i
$687$		0			0
$688$	−14.8000	+	34.3103i	−0.564246	+	1.30807i
$689$	3.32182	−	7.70084i	0.126551	−	0.293379i
$690$		0			0
$691$	−15.7344	−	7.90210i	−0.598564	−	0.300610i	0.123600	−	0.992332i	$-0.460556\pi$
$691$	−15.7344	−	7.90210i	−0.598564	−	0.300610i	−0.722164	+	0.691722i	$0.756852\pi$
$692$	−0.845488	+	4.79500i	−0.0321406	+	0.182279i
$693$		0			0
$694$	−5.16814	−	29.3100i	−0.196180	−	1.11259i
$695$	8.73495	−	29.1768i	0.331335	−	1.10674i
$696$		0			0
$697$	−48.9348	+	24.5760i	−1.85354	+	0.930881i
$698$	−14.3331	−	47.8760i	−0.542517	−	1.81213i
$699$		0			0
$700$	0.568608	−	0.763773i	0.0214914	−	0.0288679i
$701$	−9.33660	+	16.1715i	−0.352639	+	0.610788i	−0.986711	−	0.162486i	$-0.948049\pi$
$701$	−9.33660	+	16.1715i	−0.352639	+	0.610788i	0.634072	+	0.773274i	$0.281382\pi$
$702$		0			0
$703$	28.9303	+	50.1087i	1.09113	+	1.88989i
$704$	−28.2504	−	3.30200i	−1.06473	−	0.124449i
$705$		0			0
$706$	−11.6560	−	2.76252i	−0.438679	−	0.103969i
$707$	7.87574	+	5.17996i	0.296198	+	0.194812i
$708$		0			0
$709$	−22.6076	−	23.9627i	−0.849047	−	0.899938i	0.146966	−	0.989142i	$-0.453049\pi$
$709$	−22.6076	−	23.9627i	−0.849047	−	0.899938i	−0.996013	+	0.0892040i	$0.971568\pi$
$710$	18.2677	−	15.3285i	0.685576	−	0.575267i
$711$		0			0
$712$	14.4497	+	12.1247i	0.541526	+	0.454394i
$713$	0.189493	+	3.25347i	0.00709657	+	0.121843i
$714$		0			0
$715$	−6.55882	−	8.81003i	−0.245286	−	0.329476i
$716$	0.917404	−	0.107229i	0.0342850	−	0.00400734i
$717$		0			0
$718$	−20.2571	+	13.3233i	−0.755990	+	0.497222i
$719$	43.1137	−	15.6921i	1.60787	−	0.585216i	0.626852	−	0.779139i	$-0.284343\pi$
$719$	43.1137	−	15.6921i	1.60787	−	0.585216i	0.981017	+	0.193922i	$0.0621209\pi$
$720$		0			0
$721$	−4.07379	−	1.48274i	−0.151716	−	0.0552200i
$722$	−6.28670	+	1.48997i	−0.233967	+	0.0554511i
$723$		0			0
$724$	−0.0456669	+	0.784070i	−0.00169720	+	0.0291397i
$725$	−7.98355	+	8.46207i	−0.296502	+	0.314273i
$726$		0			0
$727$	6.39466	+	14.8245i	0.237165	+	0.549810i	0.994681	−	0.103007i	$-0.0328464\pi$
$727$	6.39466	+	14.8245i	0.237165	+	0.549810i	−0.757516	+	0.652817i	$0.773587\pi$
$728$	8.56403			0.317404
$729$		0			0
$730$	−27.6992			−1.02519
$731$	18.3372	+	42.5105i	0.678227	+	1.57231i
$732$		0			0
$733$	17.6698	−	18.7289i	0.652648	−	0.691767i	−0.313549	−	0.949572i	$-0.601518\pi$
$733$	17.6698	−	18.7289i	0.652648	−	0.691767i	0.966197	+	0.257805i	$0.0829993\pi$
$734$	1.13663	−	19.5151i	0.0419536	−	0.720316i
$735$		0			0
$736$	0.756375	−	0.179264i	0.0278803	−	0.00660776i
$737$	50.7756	+	18.4808i	1.87034	+	0.680750i
$738$		0			0
$739$	−16.9934	+	6.18508i	−0.625111	+	0.227522i	−0.635102	−	0.772428i	$-0.719042\pi$
$739$	−16.9934	+	6.18508i	−0.625111	+	0.227522i	0.00999089	+	0.999950i	$0.496820\pi$
$740$	3.30334	−	2.17264i	0.121433	−	0.0798678i
$741$		0			0
$742$	13.9239	−	1.62747i	0.511162	−	0.0597463i
$743$	−26.4761	−	35.5636i	−0.971314	−	1.30470i	−0.952391	−	0.304880i	$-0.901384\pi$
$743$	−26.4761	−	35.5636i	−0.971314	−	1.30470i	−0.0189230	−	0.999821i	$-0.506024\pi$
$744$		0			0
$745$	−0.687201	−	11.7988i	−0.0251771	−	0.432274i
$746$	−0.247642	−	0.207797i	−0.00906683	−	0.00760798i
$747$		0			0
$748$	3.46379	−	2.90646i	0.126649	−	0.106271i
$749$	−5.78095	−	6.12744i	−0.211231	−	0.223892i
$750$		0			0
$751$	−2.09320	−	1.37672i	−0.0763819	−	0.0502372i	0.510744	−	0.859733i	$-0.329370\pi$
$751$	−2.09320	−	1.37672i	−0.0763819	−	0.0502372i	−0.587126	+	0.809496i	$0.699741\pi$
$752$	0.857459	+	0.203222i	0.0312683	+	0.00741073i
$753$		0			0
$754$	11.9330	+	1.39477i	0.434575	+	0.0507946i
$755$	2.14057	+	3.70758i	0.0779034	+	0.134933i
$756$		0			0
$757$	21.8769	−	37.8919i	0.795129	−	1.37720i	−0.127629	−	0.991822i	$-0.540737\pi$
$757$	21.8769	−	37.8919i	0.795129	−	1.37720i	0.922757	−	0.385381i	$-0.125930\pi$
$758$	21.4515	−	28.8144i	0.779155	−	1.04659i
$759$		0			0
$760$	−5.91942	−	19.7722i	−0.214720	−	0.717215i
$761$	41.2979	−	20.7406i	1.49705	−	0.751846i	0.503366	−	0.864073i	$-0.332095\pi$
$761$	41.2979	−	20.7406i	1.49705	−	0.751846i	0.993683	+	0.112227i	$0.0357984\pi$
$762$		0			0
$763$	10.0564	−	33.5908i	0.364067	−	1.21607i
$764$	−0.658078	−	3.73214i	−0.0238084	−	0.135024i
$765$		0			0
$766$	2.18168	−	12.3729i	0.0788272	−	0.447051i
$767$	2.86531	+	1.43901i	0.103460	+	0.0519598i
$768$		0			0
$769$	11.5490	−	26.7737i	0.416469	−	0.965483i	−0.572843	−	0.819665i	$-0.694159\pi$
$769$	11.5490	−	26.7737i	0.416469	−	0.965483i	0.989311	−	0.145818i	$-0.0465814\pi$
$770$	7.27165	−	16.8576i	0.262052	−	0.607505i
$771$		0			0
$772$	−3.02306	−	1.51824i	−0.108802	−	0.0546427i
$773$	−6.90323	+	39.1502i	−0.248292	+	1.40813i	0.564429	+	0.825481i	$0.309096\pi$
$773$	−6.90323	+	39.1502i	−0.248292	+	1.40813i	−0.812721	+	0.582653i	$0.802015\pi$
$774$		0			0
$775$	2.05395	+	11.6485i	0.0737801	+	0.418427i
$776$	1.02260	−	3.41574i	0.0367094	−	0.122618i
$777$		0			0
$778$	33.3343	−	16.7411i	1.19509	−	0.600198i
$779$	14.0177	+	46.8225i	0.502238	+	1.67759i
$780$		0			0
$781$	−24.2513	+	32.5751i	−0.867779	+	1.16563i
$782$	2.69238	−	4.66333i	0.0962792	−	0.166760i
$783$		0			0
$784$	−7.39082	−	12.8013i	−0.263958	−	0.457188i
$785$	9.09774	+	1.06337i	0.324712	+	0.0379534i
$786$		0			0
$787$	−15.0251	−	3.56102i	−0.535588	−	0.126937i	−0.0460839	−	0.998938i	$-0.514674\pi$
$787$	−15.0251	−	3.56102i	−0.535588	−	0.126937i	−0.489504	+	0.872001i	$0.662822\pi$
$788$	3.22220	+	2.11927i	0.114786	+	0.0754959i
$789$		0			0
$790$	−5.99732	−	6.35679i	−0.213375	−	0.226164i
$791$	−13.1394	+	11.0253i	−0.467184	+	0.392014i
$792$		0			0
$793$	0.233973	+	0.196327i	0.00830864	+	0.00697178i
$794$	−2.18887	−	37.5815i	−0.0776801	−	1.33372i
$795$		0			0
$796$	0.110132	+	0.147933i	0.00390352	+	0.00524334i
$797$	27.5793	−	3.22356i	0.976908	−	0.114184i	0.387370	−	0.921924i	$-0.373384\pi$
$797$	27.5793	−	3.22356i	0.976908	−	0.114184i	0.589539	+	0.807740i	$0.299310\pi$
$798$		0			0
$799$	0.912204	−	0.599966i	0.0322715	−	0.0212253i
$800$	2.65111	−	0.964924i	0.0937308	−	0.0341152i
$801$		0			0
$802$	−33.1308	−	12.0586i	−1.16989	−	0.425804i
$803$	45.9002	−	10.8785i	1.61978	−	0.383896i
$804$		0			0
$805$	0.118706	−	2.03811i	0.00418385	−	0.0718340i
$806$	8.38253	−	8.88496i	0.295262	−	0.312959i
$807$		0			0
$808$	5.23093	+	12.1267i	0.184023	+	0.426614i
$809$	−1.83050			−0.0643571			−0.0321785	−	0.999482i	$-0.510245\pi$
$809$	−1.83050			−0.0643571			−0.0321785	+	0.999482i	$0.510245\pi$
$810$		0			0
$811$	−14.4506			−0.507429			−0.253715	−	0.967279i	$-0.581652\pi$
$811$	−14.4506			−0.507429			−0.253715	+	0.967279i	$0.581652\pi$
$812$	0.742743	+	1.72187i	0.0260652	+	0.0604258i
$813$		0			0
$814$	−49.4834	+	52.4493i	−1.73439	+	1.83835i
$815$	−1.49482	+	25.6651i	−0.0523613	+	0.899009i
$816$		0			0
$817$	40.2086	−	9.52962i	1.40672	−	0.333399i
$818$	13.1021	+	4.76877i	0.458104	+	0.166736i
$819$		0			0
$820$	3.13841	−	1.14229i	0.109598	−	0.0398904i
$821$	18.0379	−	11.8637i	0.629527	−	0.414046i	−0.194257	−	0.980951i	$-0.562229\pi$
$821$	18.0379	−	11.8637i	0.629527	−	0.414046i	0.823784	+	0.566904i	$0.191859\pi$
$822$		0			0
$823$	10.9193	−	1.27628i	0.380623	−	0.0444884i	0.0763694	−	0.997080i	$-0.475667\pi$
$823$	10.9193	−	1.27628i	0.380623	−	0.0444884i	0.304253	+	0.952591i	$0.401593\pi$
$824$	−3.62699	−	4.87190i	−0.126352	−	0.169721i
$825$		0			0
$826$	0.311629	+	5.35047i	0.0108430	+	0.186167i
$827$	−21.6075	−	18.1309i	−0.751367	−	0.630472i	0.184497	−	0.982833i	$-0.440934\pi$
$827$	−21.6075	−	18.1309i	−0.751367	−	0.630472i	−0.935864	+	0.352361i	$0.885379\pi$
$828$		0			0
$829$	−36.5129	+	30.6380i	−1.26815	+	1.06410i	−0.273382	+	0.961906i	$0.588142\pi$
$829$	−36.5129	+	30.6380i	−1.26815	+	1.06410i	−0.994764	+	0.102196i	$0.967413\pi$
$830$	−8.96635	−	9.50378i	−0.311227	−	0.329881i
$831$		0			0
$832$	9.90468	+	6.51441i	0.343383	+	0.225847i
$833$	−17.8208	−	4.22360i	−0.617453	−	0.146339i
$834$		0			0
$835$	−30.4862	−	3.56333i	−1.05502	−	0.123314i
$836$	−2.01791	−	3.49513i	−0.0697910	−	0.120882i
$837$		0			0
$838$	−8.71848	+	15.1008i	−0.301175	+	0.521650i
$839$	−30.8386	+	41.4235i	−1.06467	+	1.43010i	−0.168869	+	0.985639i	$0.554011\pi$
$839$	−30.8386	+	41.4235i	−1.06467	+	1.43010i	−0.895799	+	0.444459i	$0.853396\pi$
$840$		0			0
$841$	1.74623	+	5.83281i	0.0602148	+	0.201131i
$842$	−8.98039	+	4.51012i	−0.309485	+	0.155429i
$843$		0			0
$844$	−0.883866	+	2.95232i	−0.0304239	+	0.101623i
$845$	−2.82365	−	16.0137i	−0.0971364	−	0.550888i
$846$		0			0
$847$	−1.79636	+	10.1876i	−0.0617235	+	0.350051i
$848$	19.3785	+	9.73223i	0.665459	+	0.334206i
$849$		0			0
$850$	7.74080	−	17.9452i	0.265507	−	0.615515i
$851$	−3.17598	+	7.36275i	−0.108871	+	0.252392i
$852$		0			0
$853$	35.1268	+	17.6414i	1.20272	+	0.604029i	0.933336	−	0.359004i	$-0.116884\pi$
$853$	35.1268	+	17.6414i	1.20272	+	0.604029i	0.269384	+	0.963033i	$0.413180\pi$
$854$	−0.0886537	+	0.502780i	−0.00303367	+	0.0172048i
$855$		0			0
$856$	−2.04945	−	11.6230i	−0.0700487	−	0.397266i
$857$	−5.60517	+	18.7226i	−0.191469	+	0.639550i	0.807309	+	0.590129i	$0.200923\pi$
$857$	−5.60517	+	18.7226i	−0.191469	+	0.639550i	−0.998778	+	0.0494217i	$0.984262\pi$
$858$		0			0
$859$	21.3183	−	10.7065i	0.727372	−	0.365300i	−0.0462650	−	0.998929i	$-0.514732\pi$
$859$	21.3183	−	10.7065i	0.727372	−	0.365300i	0.773637	+	0.633629i	$0.218436\pi$
$860$	−0.809843	−	2.70506i	−0.0276154	−	0.0922419i
$861$		0			0
$862$	6.92807	−	9.30602i	0.235971	−	0.316964i
$863$	−12.6584	+	21.9249i	−0.430896	+	0.746334i	−0.996951	−	0.0780339i	$-0.975136\pi$
$863$	−12.6584	+	21.9249i	−0.430896	+	0.746334i	0.566055	+	0.824368i	$0.308469\pi$
$864$		0			0
$865$	18.9446	+	32.8129i	0.644134	+	1.11567i
$866$	6.51686	+	0.761712i	0.221452	+	0.0258840i
$867$		0			0
$868$	1.85519	+	0.439689i	0.0629694	+	0.0149240i
$869$	12.4347	+	8.17841i	0.421817	+	0.277434i
$870$		0			0
$871$	−15.4552	−	16.3816i	−0.523680	−	0.555068i
$872$	37.6321	−	31.5771i	1.27438	−	1.06933i
$873$		0			0
$874$	−3.68176	−	3.08936i	−0.124537	−	0.104499i
$875$	−1.31715	−	22.6146i	−0.0445278	−	0.764514i
$876$		0			0
$877$	−24.7040	−	33.1832i	−0.834194	−	1.12052i	−0.991128	−	0.132908i	$-0.957569\pi$
$877$	−24.7040	−	33.1832i	−0.834194	−	1.12052i	0.156934	−	0.987609i	$-0.449839\pi$
$878$	−22.1774	+	2.59217i	−0.748452	+	0.0874815i
$879$		0			0
$880$	23.7270	−	15.6055i	0.799838	−	0.526062i
$881$	−5.70063	+	2.07486i	−0.192059	+	0.0699038i	−0.436259	−	0.899821i	$-0.643697\pi$
$881$	−5.70063	+	2.07486i	−0.192059	+	0.0699038i	0.244200	+	0.969725i	$0.421475\pi$
$882$		0			0
$883$	13.5249	+	4.92265i	0.455148	+	0.165660i	0.559413	−	0.828889i	$-0.311027\pi$
$883$	13.5249	+	4.92265i	0.455148	+	0.165660i	−0.104265	+	0.994550i	$0.533249\pi$
$884$	−1.83383	+	0.434625i	−0.0616783	+	0.0146180i
$885$		0			0
$886$	0.980741	−	16.8387i	0.0329486	−	0.565706i
$887$	4.45102	−	4.71780i	0.149451	−	0.158408i	−0.648323	−	0.761365i	$-0.724529\pi$
$887$	4.45102	−	4.71780i	0.149451	−	0.158408i	0.797774	+	0.602957i	$0.206011\pi$
$888$		0			0
$889$	1.32120	+	3.06289i	0.0443116	+	0.102726i
$890$	−16.8541			−0.564951
$891$		0			0
$892$	−1.27732			−0.0427680
$893$	−0.385985	−	0.894813i	−0.0129165	−	0.0299438i
$894$		0			0
$895$	4.93244	−	5.22808i	0.164873	−	0.174755i
$896$	−1.40892	+	24.1902i	−0.0470687	+	0.808139i
$897$		0			0
$898$	9.65467	−	2.28820i	0.322181	−	0.0763582i
$899$	−21.8896	−	7.96717i	−0.730059	−	0.265720i
$900$		0			0
$901$	25.2474	−	9.18932i	0.841114	−	0.306141i
$902$	−50.8901	+	33.4710i	−1.69446	+	1.11446i
$903$		0			0
$904$	−23.8682	+	2.78980i	−0.793846	+	0.0927872i
$905$	3.64970	+	4.90240i	0.121320	+	0.162961i
$906$		0			0
$907$	−1.51668	−	26.0404i	−0.0503605	−	0.864657i	−0.925020	−	0.379919i	$-0.875952\pi$
$907$	−1.51668	−	26.0404i	−0.0503605	−	0.864657i	0.874659	−	0.484738i	$-0.161085\pi$
$908$	2.25389	+	1.89124i	0.0747981	+	0.0627631i
$909$		0			0
$910$	−5.86182	+	4.91865i	−0.194318	+	0.163052i
$911$	8.61747	+	9.13398i	0.285510	+	0.302622i	0.854216	−	0.519918i	$-0.174038\pi$
$911$	8.61747	+	9.13398i	0.285510	+	0.302622i	−0.568707	+	0.822540i	$0.692556\pi$
$912$		0			0
$913$	18.5906	+	12.2272i	0.615258	+	0.404662i
$914$	−17.3611	−	4.11465i	−0.574254	−	0.136101i
$915$		0			0
$916$	−3.99644	−	0.467117i	−0.132046	−	0.0154340i
$917$	6.81205	+	11.7988i	0.224954	+	0.389631i
$918$		0			0
$919$	19.5883	−	33.9279i	0.646158	−	1.11918i	−0.337875	−	0.941191i	$-0.609708\pi$
$919$	19.5883	−	33.9279i	0.646158	−	1.11918i	0.984033	−	0.177987i	$-0.0569586\pi$
$920$	1.70804	−	2.29429i	0.0563123	−	0.0756406i
$921$		0			0
$922$	2.98130	+	9.95824i	0.0981839	+	0.327957i
$923$	15.1263	−	7.59671i	0.497888	−	0.250049i
$924$		0			0
$925$	−8.34674	+	27.8800i	−0.274439	+	0.916690i
$926$	−7.23016	−	41.0043i	−0.237598	−	1.34748i
$927$		0			0
$928$	−0.964816	+	5.47174i	−0.0316716	+	0.179619i
$929$	43.1360	+	21.6637i	1.41525	+	0.710763i	0.981712	−	0.190375i	$-0.0609703\pi$
$929$	43.1360	+	21.6637i	1.41525	+	0.710763i	0.433534	+	0.901137i	$0.357267\pi$
$930$		0			0
$931$	−6.47458	+	15.0098i	−0.212196	+	0.491925i
$932$	−0.774156	+	1.79469i	−0.0253583	+	0.0587872i
$933$		0			0
$934$	19.0005	+	9.54241i	0.621715	+	0.312237i
$935$	6.11005	−	34.6518i	0.199820	−	1.13324i
$936$		0			0
$937$	2.06159	+	11.6919i	0.0673494	+	0.381957i	0.999787	+	0.0206269i	$0.00656621\pi$
$937$	2.06159	+	11.6919i	0.0673494	+	0.381957i	−0.932438	+	0.361330i	$0.882323\pi$
$938$	10.7968	−	36.0639i	0.352529	−	1.17753i
$939$		0			0
$940$	−0.0595081	+	0.0298861i	−0.00194094	+	0.000974778i
$941$	−2.49726	−	8.34141i	−0.0814082	−	0.271922i	0.907588	−	0.419861i	$-0.137921\pi$
$941$	−2.49726	−	8.34141i	−0.0814082	−	0.271922i	−0.988996	+	0.147939i	$0.952736\pi$
$942$		0			0
$943$	−4.04479	+	5.43310i	−0.131717	+	0.176926i
$944$	−4.14525	+	7.17978i	−0.134916	+	0.233682i
$945$		0			0
$946$	25.7488	+	44.5982i	0.837164	+	1.45001i
$947$	−35.0278	−	4.09416i	−1.13825	−	0.133042i	−0.473980	−	0.880536i	$-0.657183\pi$
$947$	−35.0278	−	4.09416i	−1.13825	−	0.133042i	−0.664269	+	0.747493i	$0.731257\pi$
$948$		0			0
$949$	−19.1312	−	4.53419i	−0.621026	−	0.147186i
$950$	−14.5740	−	9.58547i	−0.472843	−	0.310994i
$951$		0			0
$952$	18.8275	+	19.9560i	0.610204	+	0.646778i
$953$	22.5161	−	18.8933i	0.729369	−	0.612013i	−0.200591	−	0.979675i	$-0.564286\pi$
$953$	22.5161	−	18.8933i	0.729369	−	0.612013i	0.929959	+	0.367662i	$0.119842\pi$
$954$		0			0
$955$	−22.5912	−	18.9562i	−0.731032	−	0.613409i
$956$	−0.131795	−	2.26284i	−0.00426256	−	0.0731853i
$957$		0			0
$958$	19.9532	+	26.8018i	0.644659	+	0.865927i
$959$	−33.0069	+	3.85796i	−1.06585	+	0.124580i
$960$		0			0
$961$	6.11254	−	4.02028i	0.197179	−	0.129686i
$962$	28.2421	−	10.2793i	0.910561	−	0.331417i
$963$		0			0
$964$	0.424010	+	0.154327i	0.0136565	+	0.00497054i
$965$	−25.6153	+	6.07093i	−0.824584	+	0.195430i
$966$		0			0
$967$	−1.62289	+	27.8639i	−0.0521885	+	0.896042i	0.866036	+	0.499982i	$0.166660\pi$
$967$	−1.62289	+	27.8639i	−0.0521885	+	0.896042i	−0.918224	+	0.396061i	$0.870377\pi$
$968$	−9.94589	+	10.5420i	−0.319673	+	0.338834i
$969$		0			0
$970$	1.26185	+	2.92529i	0.0405155	+	0.0939255i
$971$	−32.8139			−1.05305			−0.526524	−	0.850160i	$-0.676505\pi$
$971$	−32.8139			−1.05305			−0.526524	+	0.850160i	$0.676505\pi$
$972$		0			0
$973$	36.1354			1.15845
$974$	24.5432	+	56.8976i	0.786416	+	1.82312i
$975$		0			0
$976$	−0.541947	+	0.574430i	−0.0173473	+	0.0183871i
$977$	0.587778	−	10.0918i	0.0188047	−	0.322864i	−0.975767	−	0.218812i	$-0.929782\pi$
$977$	0.587778	−	10.0918i	0.0188047	−	0.322864i	0.994572	−	0.104052i	$-0.0331810\pi$
$978$		0			0
$979$	27.9288	−	6.61925i	0.892609	−	0.211552i
$980$	1.04965	+	0.382042i	0.0335299	+	0.0122039i
$981$		0			0
$982$	−15.4489	+	5.62294i	−0.492994	+	0.179435i
$983$	−41.5244	+	27.3111i	−1.32442	+	0.871087i	−0.997267	−	0.0738825i	$-0.976461\pi$
$983$	−41.5244	+	27.3111i	−1.32442	+	0.871087i	−0.327157	+	0.944970i	$0.606091\pi$
$984$		0			0
$985$	29.8087	−	3.48414i	0.949784	−	0.111014i
$986$	22.9840	+	30.8728i	0.731959	+	0.983192i
$987$		0			0
$988$	0.0978075	+	1.67929i	0.00311167	+	0.0534253i
$989$	4.38685	+	3.68101i	0.139494	+	0.117049i
$990$		0			0
$991$	−20.4874	+	17.1909i	−0.650802	+	0.546088i	−0.907314	−	0.420453i	$-0.861871\pi$
$991$	−20.4874	+	17.1909i	−0.650802	+	0.546088i	0.256512	+	0.966541i	$0.417427\pi$
$992$	3.87661	+	4.10896i	0.123082	+	0.130460i
$993$		0			0
$994$	23.6389	+	15.5476i	0.749781	+	0.493139i
$995$	1.39648	+	0.330971i	0.0442713	+	0.0104925i
$996$		0			0
$997$	−42.0555	−	4.91558i	−1.33191	−	0.155678i	−0.579824	−	0.814742i	$-0.696879\pi$
$997$	−42.0555	−	4.91558i	−1.33191	−	0.155678i	−0.752087	+	0.659064i	$0.770953\pi$
$998$	5.80331	+	10.0516i	0.183701	+	0.318179i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.676.3		144
3.2	odd	2		729.2.g.b.676.6		144
9.2	odd	6		243.2.g.a.226.6		144
9.4	even	3		729.2.g.d.433.6		144
9.5	odd	6		729.2.g.a.433.3		144
9.7	even	3		81.2.g.a.58.3	yes	144
81.7	even	27		729.2.g.d.298.6		144
81.14	odd	54		6561.2.a.d.1.52		72
81.20	odd	54		243.2.g.a.100.6		144
81.34	even	27	inner	729.2.g.c.55.3		144
81.47	odd	54		729.2.g.b.55.6		144
81.61	even	27		81.2.g.a.7.3	✓	144
81.67	even	27		6561.2.a.c.1.21		72
81.74	odd	54		729.2.g.a.298.3		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.7.3	✓	144	81.61	even	27
81.2.g.a.58.3	yes	144	9.7	even	3
243.2.g.a.100.6		144	81.20	odd	54
243.2.g.a.226.6		144	9.2	odd	6
729.2.g.a.298.3		144	81.74	odd	54
729.2.g.a.433.3		144	9.5	odd	6
729.2.g.b.55.6		144	81.47	odd	54
729.2.g.b.676.6		144	3.2	odd	2
729.2.g.c.55.3		144	81.34	even	27	inner
729.2.g.c.676.3		144	1.1	even	1	trivial
729.2.g.d.298.6		144	81.7	even	27
729.2.g.d.433.6		144	9.4	even	3
6561.2.a.c.1.21		72	81.67	even	27
6561.2.a.d.1.52		72	81.14	odd	54

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.588281 - 1.36379i) q^{2} +(-0.141360 + 0.149832i) q^{4} +(-0.0932044 + 1.60026i) q^{5} +(-1.85061 + 0.438602i) q^{7} +(-2.50387 - 0.911335i) q^{8} +O(q^{10})\)	\(q+(-0.588281 - 1.36379i) q^{2} +(-0.141360 + 0.149832i) q^{4} +(-0.0932044 + 1.60026i) q^{5} +(-1.85061 + 0.438602i) q^{7} +(-2.50387 - 0.911335i) q^{8} +(2.23724 - 0.814290i) q^{10} +(-3.38752 + 2.22800i) q^{11} +(1.67851 - 0.196189i) q^{13} +(1.68684 + 2.26582i) q^{14} +(0.254067 + 4.36216i) q^{16} +(4.14727 + 3.47997i) q^{17} +(3.70167 - 3.10607i) q^{19} +(-0.226595 - 0.240177i) q^{20} +(5.03133 + 3.30916i) q^{22} +(0.651612 + 0.154435i) q^{23} +(2.41405 + 0.282162i) q^{25} +(-1.25499 - 2.17371i) q^{26} +(0.195884 - 0.339282i) q^{28} +(-2.85835 + 3.83943i) q^{29} +(1.39576 + 4.66216i) q^{31} +(1.03731 - 0.520955i) q^{32} +(2.30618 - 7.70319i) q^{34} +(-0.529392 - 3.00233i) q^{35} +(-2.07926 + 11.7921i) q^{37} +(-6.41363 - 3.22105i) q^{38} +(1.69174 - 3.92190i) q^{40} +(-4.00621 + 9.28743i) q^{41} +(7.64192 + 3.83792i) q^{43} +(0.145031 - 0.822509i) q^{44} +(-0.172714 - 0.979511i) q^{46} +(0.0578400 - 0.193199i) q^{47} +(-3.02305 + 1.51823i) q^{49} +(-1.03533 - 3.45825i) q^{50} +(-0.207877 + 0.279228i) q^{52} +(2.48138 - 4.29788i) q^{53} +(-3.24965 - 5.62856i) q^{55} +(5.03340 + 0.588321i) q^{56} +(6.91768 + 1.63952i) q^{58} +(1.58520 + 1.04260i) q^{59} +(0.124028 + 0.131462i) q^{61} +(5.53710 - 4.64618i) q^{62} +(5.37384 + 4.50919i) q^{64} +(0.157509 + 2.70433i) q^{65} +(-7.95826 - 10.6898i) q^{67} +(-1.10767 + 0.129468i) q^{68} +(-3.78311 + 2.48819i) q^{70} +(9.41216 - 3.42575i) q^{71} +(-10.9327 - 3.97917i) q^{73} +(17.3051 - 4.10138i) q^{74} +(-0.0578765 + 0.993701i) q^{76} +(5.29176 - 5.60894i) q^{77} +(-1.45390 - 3.37053i) q^{79} -7.00426 q^{80} +15.0229 q^{82} +(-2.17367 - 5.03914i) q^{83} +(-5.95539 + 6.31235i) q^{85} +(0.738510 - 12.6797i) q^{86} +(10.5124 - 2.49148i) q^{88} +(-6.65218 - 2.42120i) q^{89} +(-3.02021 + 1.09927i) q^{91} +(-0.115251 + 0.0758017i) q^{92} +(-0.297508 + 0.0347738i) q^{94} +(4.62550 + 6.21312i) q^{95} +(0.0778051 + 1.33586i) q^{97} +(3.84894 + 3.22965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more